Lemma 2.3 (Lemma 3.5 in [1]}) 

Given a Euclidean triangle \(\triangle ABC\)  with edge lengths \(a\) , \(b\) , and \(c\) , if all the angles in \(\triangle ABC\)  are at least \(\epsilon >0\) , \(\delta <\epsilon ^2/48\) , and
\(|a^{\prime }-a|\le \delta a,\quad |b^{\prime }-b|\le \delta b,\quad |c^{\prime }-c|\le \delta c,\) 
